A laser may be used as an optical transmitter that transmits light at a given wavelength. The power (i.e., amplitude) of the laser light may be modulated by corresponding modulation of the power used to drive the laser. In a directly-modulated electrically pumped semiconductor laser such as a laser diode, the electrical current that drives or pumps the laser is modulated. The relationship between the light output and the input current for such a laser may be represented using a transfer curve or L-I (light-current) curve. The set point of the L-I curve may be selected so as to maximize the linearity of the laser output in response to the modulation, within the expected range of operation of the output produced by the laser. Although the laser output may be generally linear along a significant portion of the L-I curve, the light output may attain a zero-power level when the input current falls below a threshold current level, which results in an effect known as clipping.
In a communications system where multiple channels are transmitted, such as a CATV system, multiple analog signals corresponding to the multiple channels may be combined into a wide-band multichannel RF signal, which drives a laser to produce a multichannel modulated optical signal. The multiple analog signals may include multiple modulated analog carriers that may be combined, for example, using frequency division multiplexing techniques. One or more digital signals modulated using digital modulation, such as quadrature amplitude modulated (QAM), may also be combined with the modulated analog carrier signals, for example, using subcarrier multiplexing (SCM) techniques. In some systems, for example, as many as 110 channels may be transmitted over a frequency range of about 50 MHz to 750 MHz.
Because the modulation may carry several channels of information at different frequencies, there may be a very large swing of the input drive current in either direction. When many signals are summed and are randomly distributed in both frequency and phase, the ratio of peak-to-average voltage rarely exceeds 14 dB (though with occasional higher peaks). In a CATV system, however, the downstream spectrum is not random. Peak voltage conditions may occur, for example, when a large number of carriers are harmonics of a common root frequency and the carrier phases are aligned. In that case, the time domain waveform can resemble a string of impulses spaced by a time interval equal to the period of the common root frequency. As a result of this occasionally occurring peak voltage (and thus peak drive current) condition, the laser may be driven into hard limiting, causing clipping, when a sufficient number of carriers are in phase alignment. This is particularly true in the case of directly modulated laser diodes, as described above, where a sharp knee occurs in the transfer function below which the light output reaches a zero-power level.
In other words, there will be clipping when the instantaneous sum of various signals causes the drive current to swing too far in the “downward” direction and below the threshold current that turns on the laser. When such clipping occurs, intermodulation products (i.e., clipping-induced distortion) and noise may be generated, which may result in bit errors in the optical output of the laser. When polarity of a sine wave is clipped, both even and odd order distortion products may be generated, although second order distortion products are the largest.
The even-order distortion includes composite second order (CSO) distortion products, i.e. distortion products of the type 2f1, 2f2, f2−f1, and f2+f1. In particular, CSO is a second-order distortion that combines signals at frequencies A and B, as A±B. The odd-order distortion includes composite triple beat (CTB) distortion. CTB (also known as C/CTB) is a third-order distortion product that combines signals at frequencies A, B, and C as A+B−C. For optical transmitters modulated externally with Mach-Zehnder external modulators, the nonlinearities are symmetrical and the limiting is “softer,” resulting in less clipping and primarily odd-order distortion. For directly-modulated DFB lasers, however, both CSO and CTB will show an increase when such clipping happens with sufficient frequency to be statistically significant.